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COMEDK2018MathematicsDefinite Integration

The interval I such that ₀¹ d x 1+x⁴ I is given by

Options

  1. A[0, 1 2 ]
  2. B[ 1 2 , 1 ]
  3. C[ 2 , 2]
  4. D[ 2 , 7 4 ]

Correct answer

B. [ 1 2 , 1 ]

Step-by-step solution

aligned & (b) Let I = ₀¹ 1 1+x⁴ d x & We have, 0 x 1 & 0 x⁴ 1 & 1 1+x⁴ 2 & 1 2 1 1+x⁴ 2 1 & ₀¹ 1 2 d x ₀¹ 1 1+x⁴ d x ₀¹ 1 d x & 1 2 ₀¹ 1 1+x⁴ d x 1 & I [ 1 2 , 1 ] aligned

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